The optimal homotopy-analysis method for Kawahara equation

In this paper, the optimal homotopy-analysis method is used to find the travelling-wave solution of the Kawahara equation. The method used here contains three auxiliary convergence-control parameters, which provide us with a simple way to adjust and control the convergence region of the solution. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained, which give much better approximations than those given by usual homotopy-analysis method.